Lower ionospheric resonance caused by Pekeris wave induced by 2022 Tonga volcanic eruption

The submarine volcano Hunga Tonga–Hunga Ha’apai erupted explosively on January 15, 2022, offering a unique opportunity to investigate interactions between the atmosphere and ionosphere caused by Lamb and Pekeris waves. However, the resonance of Pekeris waves has not been previously detected. In this study, we applied a multi-point monitoring approach focusing on the lower ionosphere and atmospheric electric field. Here we show observed oscillations of 100–200 s in manmade transmitter signals and the magnetic and atmospheric electric fields, which were caused by Pekeris waves. However, no corresponding changes with the period of 100–200 s in atmospheric pressure due to Pekeris waves were observed on the ground. A simulation of neutral wind revealed Pekeris waves oscillating near the mesopause, suggesting resonance. Therefore, the oscillation in atmospheric electric field is interpreted that the resonance in the lower ionosphere was projected onto the Earth's surface via a global electric circuit.


Results and discussion
The amplitudes of three VLF/LF paths were processed using a high-pass filter (HPF), with a threshold > 1.67 mHz or < 10 min, and found to vary with the arrival times of both Lamb and Pekeris waves (Fig. 2).Based on the observed VLF/LF amplitudes, the estimated propagation velocities of the Lamb and Pekeris waves were ~ 307 and ~ 235 m/s, respectively, within the ranges of ~ 300-315 m/s and ~ 230-240 m/s reported in previous studies 6,[11][12][13] .The amplitude of the VLF/LF variation due to Pekeris waves (2-4 dB) was higher than that due to Lamb waves (1-2 dB).Similarly, the amplitude of the magnetic field horizontal component (B H ) (HPF: > 1.67 mHz) at Kakioka, Japan (KAK) was lower (± 0.8 nT) when Lamb waves arrived and higher (± 1.5 nT) when Pekeris waves arrived.However, atmospheric pressure (HPF: > 1.67 mHz, P) observed by the SORATENA weather sensor at Okinawa (OKN) varied greatly around the Lamb wave arrival time (± 5 hPa), whereas amplitude variation was not observed at the Pekeris wave arrival time.The method for determining the arrival times of the Lamb (the blue vertical line) and Pekeris waves (the red vertical line) is as follows.First, we calculated the horizontal distance from the HTHH volcano to each observation site.For VLF/LF data, we adopted the shortest distance from the HTHH volcano to each propagation path.The distances for the B H at KAK, JJI-TNN, JJY60-TNN, BPC-TNN, and P at OKN were 7831.9 km, 8167.7 km, 8311.6 km, 8499.9 km, and 8032.3 km, respectively.Next, since the propagation velocity of Lamb waves estimated from VLF data was ~ 307 m/s, we calculated the propagation time of Lamb wave from distance and velocity.Therefore, the Lamb wave should arrive in the order of B H , P, JJI-TNN, JJY60-TNN, and BPC-TNN.The B H corresponds to the current in the lower ionosphere, the VLF/LF waves correspond to electron density fluctuations at a reflection altitude of approximately 90 km, and P is the atmospheric pressure at the surface of the Earth, so they are arranged in this order from top to bottom in Fig. 2. The period of the VLF variation caused by Lamb waves was the same as that of atmospheric pressure (300-500 s), although the period of B H due to Lamb waves (500-1000 s) differed from that of VLF and atmospheric pressure.In contrast, the period of the VLF variation due to Pekeris waves (200-1000 s) for the three paths was similar to that of B H (300-1000 s).There was no clear signature in the P at the arrival time of the Pekeris wave (red vertical line).This is because the amplitude of Pekeris wave at the Earth's surface is very small as suggested by theory 10 .At the D-region altitude (60-90 km), which is the reflection altitude of VLF/LF waves, the energy of Pekeris wave is trapped in the atmospheric temperature minimum region (50-110 km height), resonance occurs, and the amplitude of Pekeris wave increases.Therefore, no signatures of Pekeris waves can be seen in P at the Earth's surface, although they can be seen in VLF/LF waves at the D-region altitude.These results demonstrate that Pekeris waves exhibited slight atmospheric pressure fluctuations at the Earth's surface, although they were amplified at D-region altitudes.
Both E z (HPF: > 1.67 mHz or < 10 min) at Chiba, Japan (CHB), and B H at KAK also varied at the Pekeris wave arrival time, although the amplitudes of these fluctuations were low at the Lamb wave arrival time (Fig. 3).The   www.nature.com/scientificreports/amplitude of E z variation due to Pekeris waves (± 50 V/m) was higher than that due to Lamb waves (± 30 V/m).
The periods of the variation in E z at CHB due to Lamb and Pekeris waves were 200-1000 and 100-1000 s, respectively, similar to the B H range (300-1000 s).In contrast, little variation in atmospheric pressure was observed at CHB due to Pekeris waves, despite large variation at the Lamb wave arrival time (± 0.6 hPa).The amplitudes of Pekeris waves are low on the ground but increase at altitudes above 30 km and become even larger at D-region altitudes 6 .The electron density in the lower ionosphere is influenced by Pekeris waves, leading to changes in the electric current that in turn alter B H .The air current within the global electric circuit is conveyed by atmospheric ions; therefore, variation in the current in the lower ionosphere is hypothesized to result in an increase or decrease in the number density of atmospheric ions, thereby causing shifts in the atmospheric electric field on the ground.For Lamb waves, coherence values between VLF/LF amplitudes and other data (B H and E z ) were < 0.4, although those for Pekeris waves were higher than those for Lamb waves (Fig. 4).The common periods among multiple VLF/LF paths were 146 s (frequency: 6.8 mHz) and 205 s (4.9 mHz) between the VLF/LF amplitudes and B H , and 171 s (5.8 mHz), 205 s, and 341 s (2.9 mHz) between the VLF/LF amplitudes and B H and E z .In the F-region ionosphere, atmospheric gravity waves (GWs) originating from the HTHH volcano and migrating by Lamb wave had an impact over a long period of time (~ several hours) and over a wide area, causing TID, etc. [15][16][17][18] , although duration of GWs migrated by Pekeris wave was short 14 .The Pekeris wave did not has strong effect for the F-region ionosphere.However, in the D-region ionosphere, which is the reflection height of VLF/ LF waves, the Lamb and Pekeris waves, rather than GWs, directly changed the electron density.Pekeris wave had a relatively larger amplitude than Lamb wave at this altitude due to acoustic resonance in the neutral wind simulation (Fig. 5).Therefore, for Lamb wave, the B H and VLF/LF waves in the lower ionosphere were small and the period of fluctuation was slightly different (Fig. 2), while in the case of Pekeris wave, the B H and VLF/LF waves clearly fluctuated with the similar period.The E Z at the Earth's surface was surprisingly similar to the B H variation for both Lamb and Pekeris waves.Although atmospheric ions near the Earth's surface might change due to Lamb wave, it does not seem to result in large changes in the E z .It is possible that the lower ionosphere was greatly fluctuated by Pekeris wave with increased amplitude due to acoustic resonance, and the fluctuations in the lower ionosphere were projected to E z on the Earth's surface via a global electric circuit.Therefore, these results demonstrate that Pekeris waves cause more D-region ionospheric variation than Lamb waves, and that the D-region ionosphere and E z on the ground varied with similar periods via the global electric circuit due to Pekeris waves.
In a neutral wind simulation 14 , Lamb and Pekeris waves were observed at 11:38 UT and 13:33 UT, respectively (Fig. 5). Figure 5A shows that at an altitude of 90 km, the horizontal wind velocity of Pekeris waves is larger than that of Lamb waves.In Fig. 5B, the red areas visible at 10:00-11:40 UT, 11:40-13:30 UT, 13:30-16:00 UT, and 16:00-18:00 UT above 100 km altitudes are GWs caused by the HTHH eruption.This shows that the GWs propagated within the thermosphere and reached the midpoint of the JJY60-TNN path.It looks like this because the first GW has a fast propagation speed of about 750 m/s in the thermosphere, and the subsequent GWs have a slower propagation speed.Below 100 km altitudes, Lamb wave arrived at 11:38 UT and Pekeris waves arrived at 13:33 UT.This can be seen by the sudden change from red to blue at an altitude of 100 km.The simulated arrival time of Lamb waves was in good agreement with the time estimated from VLF/LF observations, although the simulated arrival time of Pekeris waves was earlier than that of VLF waves.These results may have been influenced by background wind, as well as the fact that atmospheric temperature and density inhomogeneities along the VLF/LF propagation paths were not included in the simulation calculations.Lamb and Pekeris wave oscillations with periods of 100-200 s were observed in the horizontal velocity at a height of 90 km.These oscillations were caused by resonance between the stratopause (~ 50 km height) and lower thermosphere.The periods of variation in both the VLF/LF amplitudes and E z for Pekeris waves were similar to that of the resonance of 100-200 s shown in the simulation.In the simulation, the horizontal velocity of Pekeris waves (− 1.26 to 3.53 m/s) was higher than that of Lamb waves (− 0.87 to 0.86 m/s), which was in good agreement with the observed amplitudes of variation in VLF/LF waves and E z , where positive (negative) horizontal velocity values indicate outward (inward) direction relative to the HTHH volcano.
This study is the first to discuss the observation of Pekeris wave resonance in the lower ionosphere in VLF/LF waves, magnetic fields, and the atmospheric electric field.Simulations of neutral wind showed similar oscillations due to Pekeris waves, which were caused by resonance between the stratopause (~ 50 km height) and the lower thermosphere.The atmospheric electric field showed similar oscillations even in ground-based observations, because oscillations near the mesopause were projected onto the Earth's surface via the global electric circuit.

Atmospheric electric field data
The atmospheric electric field has been observed with an EFM-100 field mill (Boltek) on the roof of a building on the campus of Chiba University (CHB, 35.63 °N, 140.10 °E), Japan, since 1 June, 2016.The dynamic voltage range is ± 20 kV/m with a 0.5-s sampling time.The cut-off frequency of the low-pass filter is 11 Hz.The distance from the HTHH was ~ 7790 km.

Atmospheric pressure data
We used two kinds of atmospheric pressure data.The atmospheric pressure data have been observed with a WS601-UMB Smart Weather Sensor (Lufft) at the same place of CHB with atmospheric electric field data.The data were 5-s sampling.The accuracy of the atmospheric pressure was ± 0.5 hPa.
Atmospheric pressure data at Okinawa (OKN, 27.34 °N, 128.57°E), Japan collected by the SORATENA array were provided by Weathernews Inc.The data was 1-min.sampling.The distance from the HTHH was ~ 8032 km.

Coherence calculation
Coherence, coh(ω), is defined by the following formula: where ω is the angular frequency; S xy (ω) is the cross-spectra of two discrete time signals; S xx (ω) and S yy (ω) are the spectra of x(t) and y(t), respectively; and K xy (ω) and Q xy (ω) are co-and quad-spectra, respectively 19 .Here, x(t) and y(t) denote the variation in the VLF/LF amplitudes for each path, and B H or E z , respectively.

Figure 1 .
Figure 1.Map of the region influenced by the 2022 Hunga Tonga-Hunga Ha'apai (HTHH) eruption.(A) Very low-frequency/low-frequency (VLF/LF) transmitter signals, atmospheric electric field, ground-based magnetic field, and atmospheric pressure data.Brown star indicates the HTHH volcano; blue triangles indicate VLF/LF transmitters; red diamond indicates a receiver; green rectangle indicates location of atmospheric electric field and atmospheric pressure observations at CHB; purple circle indicates location of SORATENA atmospheric pressure observations at OKN; pink triangle indicates the ground-based magnetometer at KAK; red curves indicate distances from the HTHH volcano.(B) Enlarged map of an area near observation sites shown in (A).

Figure 2 .
Figure 2. Signatures of Lamb and Pekeris waves in VLF/LF observations (high-pass filter [HPF]: > 1.67 mHz or < 10 min).(A) Horizontal (H) component of the magnetic field (B H ) at KAK (top panel), VLF/LF amplitudes for the paths JJI-TNN (second panel), JJY60kHz-TNN (third panel), and BPC-TNN (fourth panel), and atmospheric pressure data at OKN (bottom panel).(B) Waveform of B H (top panel) and wavelet spectrum (bottom panel).(C) Waveform of JJI-TNN amplitude (top panel) and wavelet spectrum (bottom panel).(D) Waveform of atmospheric pressure at OKN (top panel) and wavelet spectrum (bottom panel).Blue and red lines indicate Lamb and Pekeris wave arrival times at each site, respectively.

Figure 3 .
Figure 3. Signature of Pekeris waves in E z (HPF: > 1.67 mHz or < 10 min).(A) B H at KAK (top panel), E z at CHB (middle panel), and atmospheric pressure data at CHB (bottom panel).(B) Waveform of E z at CHB (top panel) and wavelet spectrum (bottom panel).Blue and red lines indicate Lamb and Pekeris wave arrival times at each site, respectively.

Figure 4 .
Figure 4. Coherences between VLF/LF amplitudes and other data (ground-based magnetic field at KAK and E z at CHB). (A) Coherence between VLF/LF amplitudes and B H at KAK (top panel) and coherence between the VLF/LF amplitudes and E z at CHB (bottom panel) for the Lamb wave.(B) Coherence between the VLF/LF amplitudes and B H at KAK (top panel) and coherence between the VLF/LF amplitudes and E z at CHB (bottom panel) for the Pekeris wave.

Figure 5 .
Figure 5. Simulation of horizontal velocity of neutral wind at the midpoint of the JJY60kHz-TNN path (28.3 °N, 125.2 °E) and the wavelet spectrum on January 15, 2022.(A) Horizontal velocity at a height of 90 km (top panel) and wavelet spectrum (bottom panel).(B) Horizontal velocity below a height of 200 km.Blue and red lines indicate Lamb and Pekeris wave arrival times estimated from observed VLF/LF variations, respectively.White horizontal line indicates an altitude of 90 km.To illustrate small velocities clearly, logarithms of the velocities in the unit of cm/s are taken.

2 S
xx (ω)S yy (ω) = K 2 xy (ω) + Q 2 xy (ω) S xx (ω)S yy (ω) (2) S xy (ω) = K xy (ω) − iQ xy (ω) narrowband transmitter signals.These VLF/LF signals received by a monopole antenna are then amplified, filtered, and digitized by the receiving system.The VLF/LF data are 0.1-s sampling.The digital data is automatically transmitted to a processing facility of Tohoku University, Japan.Time synchronization is achieved by a locked-GPS oscillator.To remove noise, we took a 30-s moving average for the raw data.